In Azure App Service, I can scale out to more than just 1 server instance. But I only get 1 central location for setting ENV variables - "Application settings" under "Configuration" in the Azure portal.
This means all my instances get the exact same ENV variables. That's not what I want. Instead, I would like to customize just one (or a few) instances with slightly different ENV variables ("Application settings" as Azure calls them).
Is this possible?
No, per App Service, you share all the same settings, no matter to how many instances you scale out. You say "this is not what I want" - but it is in fact what basically everybody else wants when scaling out ;)
Your alternative is to use multiple App Services. You can host them on the same App Service Plan, so you share the costs between them.